Estimating the HIV Effective Reproduction Number in the United States and Evaluating HIV Elimination Strategies

CONTEXT

The reproduction number is a fundamental epidemiologic concept used to assess the potential spread of infectious diseases and whether they can be eliminated.

OBJECTIVE

We estimated the 2017 United States HIV effective reproduction number, Re, the average number of secondary infections from an infected person in a partially infected population. We analyzed the potential effects on Re of interventions aimed at improving patient flow rates along different stages of the HIV care continuum. We also examined these effects by individual transmission groups.

DESIGN

We used the HIV Optimization and Prevention Economics (HOPE) model, a compartmental model of disease progression and transmission, and the next-generation matrix method to estimate Re. We then projected the impact of changes in HIV continuum-of-care interventions on the continuum-of-care flow rates and the estimated Re in 2020.

SETTING

United States.

PARTICIPANTS

The HOPE model simulated the sexually active US population and persons who inject drugs, aged 13 to 64 years, which was stratified into 195 subpopulations by transmission group, sex, race/ethnicity, age, male circumcision status, and HIV risk level.

MAIN OUTCOME MEASURES

The estimated value of Re in 2017 and changes in Re in 2020 from interventions affecting the continuum-of-care flow rates.

RESULTS

Our estimated HIV Re in 2017 was 0.92 [0.82, 0.94] (base case [min, max across calibration sets]). Among the interventions considered, the most effective way to reduce Re substantially below 1.0 in 2020 was to maintain viral suppression among those receiving HIV treatment. The greatest impact on Re resulted from changing the flow rates for men who have sex with men (MSM).

CONCLUSIONS

Our results suggest that current prevention and treatment efforts may not be sufficient to move the country toward HIV elimination. Reducing Re to substantially below 1.0 may be achieved by an ongoing focus on early diagnosis, linkage to care, and sustained viral suppression especially for MSM.

Analysis and optimal control of an HIV model based on CD4 count

A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign can induce backward bifurcation. It has been shown that when public enlightenment campaign is [Formula: see text] effective, the disease free equilibrium is globally asymptotically stable for [Formula: see text], whereas for [Formula: see text] the global stability of the endemic equilibrium is proved only in a special case. Time dependent controls of the intervention strategies mentioned above are incorporated into the model and the optimal control strategies with minimal implementation cost are identified. In addition, cost effectiveness analysis in the form of incremental cost effectiveness ratio is carried-out to identify the most cost effective strategies. The results suggest that out of the three non dominated strategies, the strategy of educating the newly entrants only or combination of newly entrants and susceptible individuals is very cost effective using per capita GDP of Nigeria as at 2018. However, the choice of which strategy to implement depends on budgetary allocation and resource availability.

Mathematical modeling and analysis of meningococcal meningitis transmission dynamics

Meningococcal meningitis (MCM) is one of the serious public health threats in the tropical and sub-tropical regions. In this paper, we propose an epidemic model to study the transmission dynamics of MCM with high- and low-risk susceptible populations. The model considers two different groups of susceptible individuals depending on the availability of medical resources (MR, including hospitals, health workers, etc.), which varies the infection risk. We find that the model exhibits the phenomenon of backward bifurcation (BB), which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number, [Formula: see text]. This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease. Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths, especially, in the MCM endemic regions.

Mathematical analysis of a disease-resistant model with imperfect vaccine, quarantine and treatment

In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium. It is then proved that this phenomenon vanishes either when the vaccine is assumed to be 100% potent and perfect or the Standard Incidence is replaced with a Mass Action Incidence in the model development. Furthermore, the model has a unique endemic and disease-free equilibria. Using a suitable Lyapunov function, the endemic equilibrium and disease free equilibrium are proved to be globally-asymptotically stable depending on whether the control reproduction number is less or greater than unity. Some numerical simulations are presented to validate the analytic results.

Mathematical analysis of a model for AVL-HIV co-endemicity

A model for the transmission dynamics of Anthroponotic Visceral Leishmaniasis (AVL) and human immunodeficiency virus (HIV) in a population is developed and used to assess the impact of the spread of each disease on the overall transmission dynamics. As for other vector-borne disease models, the AVL component of the model undergoes backward bifurcation when the associated reproduction number of the AVL-only sub-model (denoted by RL) is less than unity. Uncertainty and sensitivity analyzes of the model, using data relevant to the dynamics of the two diseases in Ethiopia, show that the top three parameters that drive the AVL infection (with respect to the associated response function, RL) are the average number of times a sandfly bites humans per unit time (σV), carrying capacity of vectors (KV) and transmission probability from infected humans to susceptible sandflies (β2). The distribution of RL is RL∈[0.06,3.94] with a mean of RL=1.08. Furthermore, the top three parameters that affect HIV dynamics (with respect to the response function RH) are the transmission rate of HIV (βH), HIV-induced death rate (δH), and the modification parameter for the increase in infectiousness of AIDS individuals in comparison to HIV infected without clinical symptoms of AIDS (ωH). The distribution of RH is RH∈[0.88,2.79] with a mean of RH=1.46. The dominant parameters that affect the dynamics of the full VL-HIV model (with respect to the associated reproduction number, RLH, as the response function) are the transmission rate of HIV (βH), the average number of times a sandfly bites humans per unit time (σV), and HIV-induced death rate (δH) (the distribution of RLH is RLH∈[0.88,3.94] with a mean of RLH=1.64). Numerical simulations of the model show that the two diseases co-exist (with AVL dominating, but not driving HIV to extinction) whenever the reproduction number of each disease exceeds unity. It is shown that AVL can invade a population at HIV-endemic state if a certain threshold quantity, known as invasion reproduction number, exceeds unity.

Modelling the impact of HIV on the populations of South Africa and Botswana

We develop and use mathematical models that describe changes in the South African population over the last decades, brought on by HIV and AIDS. We do not model all the phases in HIV progression but rather, we show that a relatively simple model is sufficient to represent the data and allows us to investigate important aspects of HIV infection: firstly, we are able to investigate the effect of awareness on the prevalence of HIV and secondly, it enables us to make a comparison between South Africa and Botswana. A comparison is made between two models: a model that does not reflect awareness of the devastating impact of HIV and AIDS, and a model with an added psychological awareness factor. Both models are fitted to data that reflects the incidence of HIV and AIDS within South Africa. This allows us to examine the impact of psychological awareness. We show that inclusion of the effect of awareness is absolutely necessary to arrive at a model description that satisfactorily fits the available HIV and AIDS data for South Africa. We also show that a relatively simple modelling of awareness (as opposed to more complex mathematical techniques that have been used in past studies) is sufficient to accurately describe the observed patterns in the data. Even though awareness alone is not sufficient to eradicate any disease and other control strategies should be explored and implemented concurrently with educational campaigns, we are able to conclude (through thorough model analyses procedures) that the current level of awareness in South Africa is far below the level that is effectively required to eradicate HIV from the South African population. The awareness model is also fitted to HIV-related data for Botswana and we compare the results with the South African case. Though the effect of awareness is currently estimated at a much higher level in Botswana, other factors such as poorer health care and cultural differences may play a role in limiting the ability of awareness to combat HIV in Botswana.

Global stability analysis of SEIR model with holling type II incidence function

A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (ℛ₀), is less than unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle, that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the disease is shown to be uniformly persistent whenever ℛ₀ > 1.